Your truck weight will be listed on the sticker inside the door jamb on the driver's side.
When you cycle through the information in your DIC (display below the gauges), do you have a "trans temp"? If you do, that's great because you can keep an eye on it. 3.08 is a little short, but you might be fine depending on how you tow, the conditions, elevations, hills and how much weight you also put in the truck. You really won't know till you try it. If needed, run with overdrive disengaged (still use tow/haul mode) and keep the RPM's around 3,000 and the converter locked. Your engine will be more efficient at that speed and the tranny will be cooler with it locked.
Sure, changing gears can still be done - but remember that you also have to do the front (4X4), too (or pull the front drive shaft). You could always add a tranny cooler - should be less $$ than changing gears and would be highly recommended since you're approaching the upper range of your tow limit.